B+90+(b+45)+3/2b+(2b-90)=540

Solution for B+90+(b+45)+3/2b+(2b-90)=540 equation:

+90+(B+45)+3/2B+(2B-90)=540

We move all terms to the left:

+90+(B+45)+3/2B+(2B-90)-(540)=0


Domain of the equation: 2B!=0

B!=0/2

B!=0

B∈R


We add all the numbers together, and all the variables

(B+45)+3/2B+(2B-90)-450=0

We get rid of parentheses

B+3/2B+2B+45-90-450=0

We multiply all the terms by the denominator


B*2B+2B*2B+45*2B-90*2B-450*2B+3=0

Wy multiply elements

2B^2+4B^2+90B-180B-900B+3=0

We add all the numbers together, and all the variables

6B^2-990B+3=0

a = 6; b = -990; c = +3;
Δ = b2-4ac
Δ = -9902-4·6·3
Δ = 980028
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$B_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{980028}=\sqrt{36*27223}=\sqrt{36}*\sqrt{27223}=6\sqrt{27223}$
$B_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-990)-6\sqrt{27223}}{2*6}=\frac{990-6\sqrt{27223}}{12}
$
$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-990)+6\sqrt{27223}}{2*6}=\frac{990+6\sqrt{27223}}{12}
$